This requires the add-on from Gravity forms called Advanced Post Creation Add-on. A template post-submission form can be found here in the Gravity Forms Template Folder. Importing this .json file will get you halfway there.
The PIE Calendar plugin uses posts and turns them into a calendar. It can work with Custom Post Types as well. An example of the calendar can be seen in this website where a calendar is set up. By following these directions, you can also set it up to submit events from the front end with a Gravity form as…